Mathematical modeling of soybean drying by a fractional-order kinetic model

2017 ◽  
Vol 41 (2) ◽  
pp. e12655 ◽  
Author(s):  
Douglas Junior Nicolin ◽  
Rafael Oliveira Defendi ◽  
Diogo Francisco Rossoni ◽  
Luiz Mario de Matos Jorge
Keyword(s):  
Mathematical Modeling ◽  
Kinetic Model ◽  
Fractional Order ◽  
Order Kinetic ◽  
Order Kinetic Model

scholarly journals Investigation of Seeds and Peels of Citrullus colocynthis as Efficient Natural Adsorbent for Methylene Blue Dye

Processes ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 1279
Author(s):  
Wafa Mohammed Alghamdi ◽  
Ines El Mannoubi
Keyword(s):  
Methylene Blue ◽  
Kinetic Model ◽  
Langmuir Isotherm ◽  
Order Kinetic ◽  
Citrullus Colocynthis ◽  
Natural Adsorbent ◽  
Spontaneous Process ◽  
Equilibrium Data ◽  
Order Kinetic Model ◽  
Mb Adsorption

Natural adsorbents as low-cost materials have been proved efficient for water remediation and have significant capacity for the removal of certain chemicals from wastewater. The present investigation aimed to use Citrullus colocynthis seeds (CCSs) and peels (CCPs) as an efficient natural adsorbent for methylene blue (MB) dye in an aqueous solution. The examined biosorbents were characterized using surface area analyzer (BET), scanning electron microscope (SEM), thermogravimetric analyzer (TGA) and Fourier transform infra-red (FT-IR) spectroscopy. Batch adsorption experiments were conducted to optimize the main factors influencing the biosorption process. The equilibrium data for the adsorption of MB by CCSs were best described by the Langmuir isotherm followed by the Freundlich adsorption isotherms, while the equilibrium data for MB adsorption by CCPs were well fitted by the Langmuir isotherm followed by the Temkin isotherm. Under optimum conditions, the maximum biosorption capacity and removal efficiency were 18.832 mg g−1 and 98.00% for MB-CCSs and 4.480 mg g−1 and 91.43% for MB-CCPs. Kinetic studies revealed that MB adsorption onto CCSs obeys pseudo-first order kinetic model (K1 = 0.0274 min−1), while MB adsorption onto CCPs follows the pseudo-second order kinetic model (K2 = 0.0177 g mg−1 min−1). Thermodynamic studies revealed that the MB biosorption by CCSs was endothermic and a spontaneous process in nature associated with a rise in randomness, but the MB adsorption by CCPs was exothermic and a spontaneous process only at room temperature with a decline in disorder. Based on the obtained results, CCSs and CCPSs can be utilized as efficient, natural biosorbents, and CCSs is promising since it showed the highest removal percentage and adsorption capacity of MB dye.

Dyeing mechanism and photodegradation kinetics of gardenia yellow natural colorant

2020 ◽  
pp. 004051752095848
Author(s):  
Huiyu Jiang ◽  
Xiaodong Hu ◽  
Asfandyar Khan ◽  
Jinbo Yao ◽  
Muhammad Tahir Hussain
Keyword(s):  
Kinetic Model ◽  
Cotton Fabric ◽  
Reaction Rate Constant ◽  
Second Order ◽  
Order Kinetic ◽  
Natural Colorant ◽  
Yellow Solution ◽  
Order Kinetic Model ◽  
Pseudo Second Order ◽  
Dyeing Rate

In this study, gardenia yellow solution is used to dye 100% cotton fabric. The dyeing rate curve and adsorption isotherms were recorded to explore the thermodynamic model and to calculate the corresponding parameters. A definite concentration of gardenia yellow solution was placed under the xenon arc lamp for irradiation to test its photodegradability. Absorbance of the solution was measured at different degradation times and the corresponding varying curve of the absorbance was drawn to explore the photodegradation reaction order of the natural colorant and consistent parameters were calculated. The experimental results proved that the dyeing of cotton fabric with gardenia yellow colorant followed the pseudo second order kinetic model whereas adsorption isotherm followed the Langmuir model and the photodegradation process followed the second order kinetic model. Values of different parameters were calculated: reaction rate constant k = 2.26 × 10–3 (mg · L−1)1−m h−1, the correlation coefficient R2 = 0.994, and half decay time t1/2 = 5.82 h.

Iron Chelation by Polyamidoamine Dendrimers: A Second-Order Kinetic Model for Metal–Amine Complexation

2011 ◽  
Vol 115 (46) ◽  
pp. 13534-13540 ◽  
Author(s):  
Michael R. Mankbadi ◽  
Mohamed A. Barakat ◽  
Mohamed H. Ramadan ◽  
H. Lee Woodcock ◽  
John N. Kuhn
Keyword(s):  
Kinetic Model ◽  
Iron Chelation ◽  
Second Order ◽  
Order Kinetic ◽  
Polyamidoamine Dendrimers ◽  
Order Kinetic Model ◽  
Metal Amine

scholarly journals Kinetic Modeling of a Heterogeneous Fenton Oxidative Treatment of Petroleum Refining Wastewater

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Diya'uddeen Basheer Hasan ◽  
Abdul Aziz Abdul Raman ◽  
Wan Mohd Ashri Wan Daud
Keyword(s):  
Kinetic Model ◽  
Direct Conversion ◽  
Order Kinetic ◽  
Initial Oxidation ◽  
Oxidation Step ◽  
Kinetic Rate Constants ◽  
Order Kinetic Model ◽  
Generalized Kinetic Model ◽  
Petroleum Refinery Effluent ◽  
Kinetics Of

The mineralisation kinetics of petroleum refinery effluent (PRE) by Fenton oxidation were evaluated. Within the ambit of the experimental data generated, first-order kinetic model (FKM), generalised lumped kinetic model (GLKM), and generalized kinetic model (GKM) were tested. The obtained apparent kinetic rate constants for the initial oxidation step (k2′), their final oxidation step (k1′), and the direct conversion to endproducts step (k3′) were 10.12, 3.78, and 0.24 min−1for GKM; 0.98, 0.98, and nil min−1for GLKM; and nil, nil, and >0.005 min−1for FKM. The findings showed that GKM is superior in estimating the mineralization kinetics.

Kinetic Studies on Sorption of Textile Dyes Using Lamina and Petiole Parts of Eichhornia crassipes

2008 ◽  
Vol 3 (2) ◽  
Author(s):  
S Renganathan ◽  
R Venkatakrishnan ◽  
P Gautam ◽  
Lima Rose Miranda ◽  
M Velan
Keyword(s):  
Diffusion Coefficient ◽  
Kinetic Model ◽  
Eichhornia Crassipes ◽  
Kinetic Studies ◽  
Reactive Dye ◽  
The Other ◽  
Order Kinetic ◽  
Uptake Capacity ◽  
Fast Red ◽  
Order Kinetic Model

Sorption capacity of two different parts of Eichhornia crassipes such as Lamina and Petiole on a Basic dye (Basic Aurophine-O), Acidic dye (Acid Fast Red-A) and Reactive dye (Brill Red-5B) was studied in a batch system. The maximum equilibrium uptake capacity of petiole was 25.5 mg/g for Basic Aurophine-O, 23.1 mg/g for Acid Fast Red-A and 0.18 mg/g for Brill Red-5B. The equilibrium uptake capacity of petiole was found to be more in Basic Aurophine-O dye when compared to all other dyes studied. The maximum equilibrium uptake capacity of lamina was 27.0 mg/g for Basic Aurophine-O, 25.2 mg/g for Acid Fast Red-A and 4.2 mg/g for Brill Red-5B. The equilibrium uptake capacity of lamina was found to be more in Basic Aurophine-O when compared to Brill Red-5B and Acid Fast Red-A dyes studied in the present investigation. From the result, it was observed that the uptake capacity of dyes using E. crassipes part Lamina was found to be more when compared to the other E. crassipes part of Petiole used in the present study. Sorption results were found to be fitted very well with the Pseudo-second order kinetic model when compared to Pseudo-first order kinetic model. The intra particle diffusion coefficient (Ki) and diffusion coefficient (Di) obtained for the removal of dyes studied using Lamina was found to be more when compared to the other part of Petiole. The polynomial equations are developed and can be used as a ready reckoner equation to find out the percentage color removal of dyes studied in the present investigation at different period of time intervals.

Second-Order Kinetic Model for the Sorption of Cu(II) Ions in Aqueous Solutions of Zeolite NaA

2012 ◽  
Vol 560-561 ◽  
pp. 1174-1177 ◽  
Author(s):  
Dimitar Petrov Georgiev ◽  
Bogdan Iliev Bogdanov ◽  
Yancho Hristov ◽  
Irena Markovska
Keyword(s):  
Kinetic Model ◽  
Aqueous Solutions ◽  
Kinetic Parameters ◽  
Linear Equations ◽  
Linear Method ◽  
Second Order ◽  
Order Kinetic ◽  
Zeolite Naa ◽  
Order Kinetic Model ◽  
Pseudo Second Order

In this study, the sorption of Cu(II) ions in aqueous solutions of Zeolite NaA by performing batch kinetic sorption experiments. The equilibrium kinetic data were analyzed using the pseudo-second-order kinetic model. A comparison was made of the linear least-squares method and nonlinear method of the widely used pseudo-second-order kinetic model for the sorption of Cu(II) ions of Zeolite . Four pseudo-second-order kinetic linear equations are discussed. Kinetic parameters obtained from the four kinetic linear equations using the linear method differed but they were the same when using the non-linear method. Kinetic parameters obtained from four kinetic linear equations using the linear method differed. Equation type 1 pseudo-second-order kinetic model very well represented the kinetic of the adsorption Cu(II) ions by Zeolite NaA. Equation type 4 exhibited the worst fit. Present investigation showed that the non-linear method may be a better way to determine the kinetic parameters.

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